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Physical Review A

Shift and broadening in attenuated total reflection spectra of the hyperfine-structure-resolved D2 line of dense rubidium vapor

Rikio KONDO, 賢 東條, Takashi Fujimoto, Masahiro Hasuo

Published Jun 8, 2006• 32 citations
Publisher

Abstract

We have observed attenuated total reflection at a glass/rubidium vapor interface in high precision. The atom density was from $3.8\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}3.7\ifmmode\times\else\texttimes\fi{}{10}^{21}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{\ensuremath{-}3}$ and the angle of incidence was from 48.4 to 64.8\ifmmode^\circ\else\textdegree\fi{}. Redshift and broadening of the reflection spectra were observed. The redshift depended on atom density, angle of incidence, light polarization and hyperfine structure. The observed broadening was attributed to the self-broadening of the resonance line. Calculation based on the Fresnel formula with a local index for the susceptibility of the vapor, which included the Lorentz local field correction and the modification of the wave vector of the evanescent light by the optically dense atomic vapor, was found to be in reasonable agreement with the experimental results.

DOI
10.1103/physreva.73.062504

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Scientific Reports•Nov 4, 2021•7 citations
We have observed attenuated total reflection at a glass/rubidium vapor interface in high precision. The atom density was from 3.8\ifmmode×\else\texttimes\fi1020to3.7\ifmmode×\else\texttimes\fi1021m\ensuremath−33.8\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}3.7\ifmmode\times\else\texttimes\fi{}{10}^{21}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{\ensuremath{-}3}3.8\ifmmode×\else\texttimes\fi1020to3.7\ifmmode×\else\texttimes\fi1021m\ensuremath−3 and the angle of incidence was from 48.4 to 64.8\ifmmode^\circ\else\textdegree\fi{}. Redshift and broadening of the reflection spectra were observed. The redshift depended on atom density, angle of incidence, light polarization and hyperfine structure. The observed broadening was attributed to the self-broadening of the resonance line. Calculation based on the Fresnel formula with a local index for the susceptibility of the vapor, which included the Lorentz local field correction and the modification of the wave vector of the evanescent light by the optically dense atomic vapor, was found to be in reasonable agreement with the experimental results.
Absorption spectrum of the evanescent light at a glass/Rb vapor interface has been observed with atom density from 9 ×10 19 m -3 to 5 ×10 20 m -3 . Absorption is as high as 60% at the peak of a hyperfine structure split line. The absorption spectrum of the experiment is compared with that of the calculation based on Fresnel's relation on the assumption of a homogeneous electric susceptibility of the vapor. Near the critical angle the calculation which incorporates the Lorentz–Lorenz local-field correction reproduces the experimental red shift only partly.
A theory of selective reflection (SR) of a light beam from the interface of a dielectric medium and a dense atomic vapor is presented. Following another earlier work on this subject [J. Guo et al., Opt. Commun. 110, 732 (1994)], we calculate the atomic density matrix and the transmitted field in the vapor self-consistently. We extend our previous theory to include an attractive atom-dielectric wall interaction and multiple atomic transitions. We examine the limits at which the conventional SR theories, which are based on the assumption of a plane-wave field in the vapor, start to fail. It is shown that at or above vapor densities of order 1017{10}^{17}1017/cm3{\mathrm{cm}}^{3}cm3, the frequency shifts of the SR line shape due to the local-field correction (Lorentz-Lorenz shift), the atom-wall interaction, and the nonexponential attenuation of the field in the vapor can have comparable orders of magnitude, and the proper determination of all these effects is essential for calculating the correct SR signals. A comparison of the theoretical SR spectra with an experimental result for a Rb vapor with a density of order 1017{10}^{17}1017/cm3{\mathrm{cm}}^{3}cm3 is also presented. \textcopyright{} 1996 The American Physical Society.
The Lorentz-Lorenz equation predicts that the dispersion feature of an isolated optical resonance should have a density-dependent frequency shift toward the red end of the spectrum. We have investigated the dispersion feature experimentally by observing the frequency dependence of the Fresnel reflection (selective reflection) from the boundary between a dense atomic potassium vapor and the window of the vessel containing the vapor. We find that the selective-reflection features of both the S1/2-P1/2 (770.1 nm) and S1/2-P3/2 (766.7 nm) lines of potassium shift increasingly toward the red and broaden as the number density of the vapor is increased to 2 × 1017 atoms/cm3. We compare the results of the experiment to theoretical predictions for the selective reflection. The broadening is well described by conventional binary collision theory; however, the observed red shift of both of the lines is somewhat larger than that predicted by the Lorentz-Lorenz equation. It is possible that other mechanisms that lead to frequency shifts are occurring.
We calculate the reflection coefficient for a light beam incident on the interface between a dielectric and a resonant atomic vapor to first order in the dipole polarization in the vapor. The angle of incidence and the polarization direction are chosen arbitrarily, and saturation is fully accounted for. The atoms are supposed to get deexcited at collisions with the surface. The resulting transient behavior of atoms leaving the surface is responsible for a nonlocal response. This spatial dispersion near the surface is known to produce a natural-linewidth-limited resonance in the vapor reflection coefficient at normal incidence. Our analysis shows that this sub-Doppler structure is broadened by the residual Doppler effect for non-normal incidence. This structure disappears at the critical angle for total internal reflection, where one predicts a conventional Voigt-type dispersion response, based on the complex-refractive-index approach. We also calculate the saturation broadening of the atomic response for large intensities. Beyond the critical angle, the spectral response suddenly shifts from dispersion to absorption line shapes. In the case of total internal reflection, the spatial dispersion leads to an additional Lorentzian broadening, which results from an effective imaginary Doppler shift at passage through the evanescent wave (transit-time broadening).
Abstract Coherent narrow resonances in a homogeneously broadened contour of selective reflection from the interface between a cell window and high-density atomic rubidium vapor, where the dipole broadening greatly exceeds the Doppler width of the unresolved components of rubidium D2 line, are discussed. The formation of coherent resonances is caused by the coherent scattering of probe and pump optical fields from the oscillations of populations of the ground and excited states of atoms at the beat frequency. The width of each resonance depends on the population difference decay rate. Within a simple model conditions are found for observing resonances with a Lorentzian spectral profile. The experimentally recorded coherent resonances are described by a Lorentz function with fitting parameters in the form of amplitude, width, and spectral baseline. In the limit of zero optical saturation the measured half-width of a coherent resonance (HWHM) γres/2π is about 52 MHz, which greatly exceeds the radiative decay rate of the rubidium excited state 5P3/2.
Various efforts have been made to determine the polarization state of evanescent waves in different structures. The present study shows the reliability of magneto-optical spectroscopy of D1 and D2 lines of rubidium metal and polarization-dependent transitions to investigate and trace the changes in the polarization state of evanescent fields during total internal reflection over different angles. For this purpose, we design and fabricate atomic- evanescent Rb vapor cells and examine the effect of polarization changes of evanescent waves, depending on the propagation direction of evanescent waves in anisotropic rubidium vapor media under 88 mT external magnetic field by different configurations theoretically and experimentally. The results confirm the dependency of allowed [Formula: see text] transitions on the magneto optical configuration as a tool to determine changes in the polarization of evanescent waves in more complicated wave states in anisotropic media.